Linear chance constraints are used to compute bounded collision-free trajectories with dynamic obstacles in [1]}. Axelrod et al. [2]} focus exclusively on obstacle uncertainty. They formalize a notion of “shadows", which are the geometric equivalent of confidence intervals for uncertain obstacles. The shadows fundamentally give rise to loose bounds but the computational complexity of bounding the collision probability is greatly reduced. Uncertain obstacles are modelled as polytopes with Gaussian-distributed faces in [3]}. Planning a collision-free path in the presence of “risk zones" is considered in [4]} by penalizing the time spent in these risk zones. Risk contour maps which give the risk
information (uncertainties in location, size and geometry of obstacles) in uncertain environments are used in [5]} to obtain safe paths with bounded risks. A related approach for randomly moving obstacles is presented in [6]}. Formal verification methods have also been used to construct safe plans [7]}, [8]}.
